Notes:
A Lie groupoid can be considered as a generalization of a Lie group, but it does have the additional requirements for the groupoid’s structure maps that do not have corresponding conditions in the simpler case of the Lie group structure. Because the object space G0subscriptG0G_{0} of a Lie groupoid ?Lsubscript?L\mathcal{G}_{L} is a smooth manifold, G0subscriptG0G_{0} is denoted in this case as MMM.